$J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 5x - 3$ and $ JT = 2x + 21$ Find $CT$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {5x - 3} = {2x + 21}$ Solve for $x$ $ 3x = 24$ $ x = 8$ Substitute $8$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 5({8}) - 3$ $ JT = 2({8}) + 21$ $ CJ = 40 - 3$ $ JT = 16 + 21$ $ CJ = 37$ $ JT = 37$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {37} + {37}$ $ CT = 74$